Published Paper

Inserted: 18 feb 2025
Last Updated: 13 apr 2026

Journal: Nonlinear Analysis
Volume: 261
Year: 2025
Doi: https://doi.org/10.1016/j.na.2025.113908

Abstract:

We prove sharp boundary regularity of solutions to nonlocal elliptic equations arising from operators comparable to the fractional Laplacian over Reifenberg flat sets and with null exterior condition. More precisely, if the operator has order $2s$ then the solution is $C^{s-\varepsilon}$ regular for all $\varepsilon>0$ provided the flatness parameter is small enough. The proof relies on an induction argument and its main ingredients are the construction of a suitable barrier and the comparison principle.